\centerline{\small\it
Edelstein Center for the History and Philosophy of Science, The Hebrew
University}

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\centerline{\small\it
Jerusalem, Israel}

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\centerline{\small\it
(shahardo@cc.huji.ac.il)}

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date)}{(revised date)}

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Abstract:}

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Time's apparent ``flow" is often dismissed in
physical theory. We propose to take it as a real property of reality and show
how the addition of this assumption to physics' prevailing postulate yields, a
new framework within which relativity and quantum theories are in harmony with
one another.
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\section{INTRODUCTION}

For more than a century since the advent of relativity
theory and quantum mechanics, the two theories have made tremendous progress,
yet the conflict between their principles has only become sharper. A more
fundamental theory, within which the two theories would naturally fit in as
special cases, is not yet at sight.

Unrelated to this stalemate, a much older debate goes on
concerning the nature of time. Why does time, unlike space, appear to be
``flowing"? And why are certain processes asymmetric in time, in contrast
to their spatial symmetry?

We submit that addressing the latter issue may yield a
new resolution to the former. In what follows we propose that time's apparent
``flow" is real, and then proceed to show how this assumption might enable
quantum mechanics and relativity theory to begin merging into a new theory.

This is a highly speculative work. We claim neither rigor
nor certainty. It is after several years of working on specific problems that
we feel that time is ripe for a more daring synthesis, even at the cost of
being loose.

The structure of our theory is like that of any
scientific theory. At the basis we introduce a few known principles of
prevailing physical theories as postulates, plus one new assumption. In return
we hope to derive {\it i}) conclusions already accepted as correct although not
assumed, and, {\it ii}) testable predictions. Unfortunately, nothing like {\it
ii}) has been yielded by our theory yet, to say nothing of confirmation,
otherwise we would be singing it from all the roofs. Yet, because something
like {\it i}) seems to have emerged from time to time along our search, we dare
take it as a hint that we may be on the right track.

\section{
``BLOCK UNIVERSE" OR ``PRESENTISM"? }

Mainstream physics' account of time is known as the
``Block Universe." Rooted in the theory of relativity, it portrays the
universe as a four-dimensional continuum in which all past, present and future
events have the same degree of existence along time, just as different
locations coexist along space. All three-dimensional objects are ``slices"
of four-dimensional world-lines, extending from past to future. An object's
motion is a curvature on its world-line.

The rival model, ``Presentism," tries to account for
our perception of time by asserting that only present events are real. States
merely appear and vanish, consecutively, ``time" being just the sum of
these changes. Referring to time as a dimension, so goes this view, is only a
useful metaphor, and relativistic notions like ``spacetime" and ``world
lines" are mere abstractions. Only the ``Now" is real, and is the
same everywhere. Of course, in order to avoid conflict with relativity (see \cite{Godel49}),
Presentism must concede that this simultaneity can never be observed. This
concession is not necessarily a disadvantage of the model, as unobservable
elements of nature feature in many respectable theories.

Both models come with a price. The former dismisses our
subjective sensation of time, while the latter gives up full conformance with
relativity, yet both are self-consistent. It is only when trying to blend the
two notions to mach both subjectivity and relativity, that serious paradoxes
ensue. For example, taking time to be the fourth dimension {\it together with}
an objective ``Now" is bound to imply a yet higher time dimension within
which the ``Now" is supposed to proceed. Only the two extremes in their
pure form seem to be viable, the Block Universe being mainstream physics'
choice while Presentism is opted by a minority.

The option we seek is different. We wish to preserve the
essential elements of relativity theory, but we also want to take the
``Now" as a key to a deeper layer of physical reality. And, of course, we
hope to avoid the paradoxes that often follow such a double standard. We name
the proposed model the Spacetime Dynamics theory, as it suggests that spacetime
itself is subject to evolution.

Let us, then, first point out those essential elements of
relativity theory that are likely to remain within any future theory. First is
the notion of a four-dimensional spacetime. General relativity's interpretation
of gravity as a curvature of spacetime is one of the theory's greatest achievements,
well-supported by all experimental tests. Even some yet-unknown aspects of
spacetime, such as its form in a black hole singularity or at the Planck scale,
give valuable leads for future research. Similarly constructive is the notion
of a world-line, portraying any object as a four-dimensional line extending
from past to future. The world-line notion provides, {\it e.g.}, the best
understanding of relativistic contraction (see \cite{ED05}). At the micro
level, Feynmann's diagrams, especially the idea of an anti-particle being a
particle that moves backwards in time \cite{Feynman48}, testifies to the great
heuristic potential of the 4-D spacetime. Two modern interpretations of QM,
namely, Aharonov's \cite{Aharonov95} and Cramer's \cite{Cramer86}, elegantly
invoke spacetime zigzags in order to account for some of the peculiarities of
quantum phenomena (see \cite{Elitzur90}). All these are promising elements of
the relativistic spacetime, which we intend to preserve within the Spacetime
Dynamics theory.

It is with respect to two other assertions that the Block
Universe model turns out to be very awkward:

\begin{enumerate}

\item
There is no objective ``Now" moving from one minute to another. Each event
is ``Now" for its observer. Similarly, ``past" and ``future" are
relative terms just as, say, ``East" and ``West."

\item
At any moment, future events are as real as present events and as fixed as past
events. It is only because no information comes from the future (due to the
second law of thermodynamics, which can be assumed even within the Block
Universe framework) that future events seem not to exist.

\end{enumerate}

These assertions have odd consequences. Every person,
rather than being just one person undergoing many events, is supposed to be a
series of equally-existing momentary persons, each residing in its moment.
Every such a momentary self is a 3-D ``slice" of the 4-D world-line, which
in itself does not move or change. Every momentary self possesses memories of
the previous ones, thereby having the illusion that he or she is one and the
same person who has been through all past events. Whatever is going to happen
in the future, even one's own actions, ``already" exists, albeit unknown,
together with the future selves, and cannot be changed or avoided, just like
past events.\footnote{This account, it should be stressed, is not just one
possibole interpretatin ofrelativity theory but an inevitable part of it. This was Einstein's own
view; see \cite{Davies95} for a detailed discussion.}

This account is awkward not only in terms of ordinary
experience but in the quantum context as well. In earlier publications we have
presented three results that, although not disproving the Block Universe,
seriously undermine it:

\begin{enumerate}

\item
{\it ``Hidden variables must be forever-hidden variables"}\ Consider a
photon at time $t$ after being emitted from its source. Its wave function
describes its position as a superposition, which will give its place
(``collapse") to a definite position only upon measurement. Now quantum
theory can only give probabilities for that future position. In order to assume
that the future position is pre-determined already at $t$, one has to invoke
hidden variables of some sort. However, elsewhere \cite{ED05} we have given a
very straightforward proof for the following. {\it In any theory within which
relativity remains valid, quantum hidden variables must never be observed,
since observing them is bound to produce violations of relativistic
invariance}. Such invocation of something that must exist but never be observed
-- properties that even the $19^{th}$-Century ether was not claimed to have --
places hidden variables in the realm of religion rather than
science\footnote{``For there shall no man see me, and live." -- Exodus 33:
20.}. It is, therefore, the combined lesson of both QM and relativity that
gives us an important hint: There are future events that can never be predicted
by a present state. Would it not be reasonable, then, to doubt whether such
future events exist in the first place?

\item

{\it
The Indeterminacy-Asymmetry Entailment}\ If quantum theory indeed reveals a
genuinely indeterminate element that takes part in any interaction, then, in
any closed system, an arrow of time must eventually emerge, regardless of the system's
initial conditions and concurring with the time arrow of the universe outside,
from which the system is supposed to be shielded \cite{Elitzur99a}. Hence, the
Block Universe assertion ``the future determines the present just like the
past," is simply wrong. True, the question of determinism {\it vs.}
indeterminism has not been decisively resolved yet, but given our above proof
that ``hidden variables must be forever-hidden variables," strong
determinism is a metaphysical theory. Consequently, by the
Indeterminacy-Asymmetry Entailment, an initial low-entropy state can causally
bring about the final high-entropy state but {\it not vice versa}. This
conclusion strongly undermines the Minkowskian picture of future events
coexisting in time alongside with the present.

\item
{\it Quantum Mutual measurements Entailing Inconsistent Histories}\ As odd as
the famous quantum effects are known to be, e.g., single-particle interference
and the EPR experiment, they yield self-consistent evolutions. We have shown, however,
a few cases where even this consistency does not hold \cite{Dolev00}. When the
quantum measurement is delayed, such that one particle ``measures" another
particle before the macroscopic device completes the measurement, something
intriguing occurs: The outcome is self-contradictory -- a quantum version of
the Liar Paradox \cite{ED05}. These results further undermine the notion of a
fixed spacetime within which all events maintain simple causal relations.
Rather, it seems that quantum measurement can sometimes ``rewrite" a
process's history.

\end{enumerate}

Something, then, seems to be flawed with the orthodox
view of time as a mere dimension. Bearing in mind that the nature of time has
an immediate bearing on many physical issues, it is reasonable to expect that a
deeper theory of time will shed a new light on some other conundrums in the
foundations of physics.

\section{THE
ASSUMPTION: BECOMING IS REAL}

The Spacetime Dynamics theory makes one new assumption:

\proclaim{The
Assumption Of Becoming:}{What an observer perceives as ``Now" is a special
moment which marks the genuine creation of new events. World-lines objectively
``grow" in the future direction. At any moment in time which an observer
perceives as ``Now," future events are not only unknown but {\it
objectively inexistent}, to be created later as the ``Now" advances.}

Notice that the Block Universe is preserved as a special
case in this model: Spacetime with its world lines exist in the past, but not
in the future. Broad \cite{Broad23} and Sider \cite{Sider01} refers to this as
the ``Growing Block Universe."

in what follows, the new theory's postulates will be all
the prevailing physical principles and effects ,plus this new assumption. Let
us follow their consequences.

\section{MACH'S
PRINCIPLE EXTENDED: SPACETIME ITSELF UNFOLDS WITH THE UNFOLDING OF NEW EVENTS}

Our first postulate is a simple principle due to Mach
\cite{Mach60}:

\proclaim{Postulate
A:}{Space and time are inconceivable in the absence of events.}

The logical consequence of the Becoming Assumption and
Postulate A is that we cannot conceive of new events being added to some empty
spacetime in the future. Rather, spacetime itself must be ``growing" in
the future direction, alongside with the ``growth" of the world-lines and
the creation of new events. Hence,

\proclaim{Consequence
1:}{Any moment in time which an observer perceives as ``Now" is simply the
edge of time: {\it Nothing}, not even spacetime, exists beyond it.}

While it is easy to illustrate spacetime with the
familiar Minkowski diagram, our alternative model eludes graphic
representation. We could draw a Minkowski diagram with an upper boundary
representing the ``Now", where all world-lines simply end, but that would
be misleading: The empty surface above the ``Now" would still have the
diagram's spatial dimensions. It is simply impossible so portray the absence of
space! But it is this very difficulty that should give us an insight into the
reason why physical theory has been stagnating so long in this respect. Space,
as Kant \cite{Kant1787} has proven, underlies any possible though; we cannot
think even the most abstract thought without implicitly assuming some
underlying space. Bergson \cite{Bergson11} has further shown that this problem besets
modern physics' theorizing about time: We keep ``spatializing" time. One
should be aware of this inherent limitation of human thinking when seeking to
transcend the present account of space and time.

\section{COSMOLOGY
EXTENDED: SPACETIME EXPANDS IN THE TIME DIRECTION TOO}

It cannot escape us that Consequences1 has a strong affinity to mainstream
cosmology's standard model:

But then, if the advancing ``Now" is the edge of
time beyond which no spacetime exists, then spacetime must be expanding in the
time direction too. We move away from past events, perhaps, not unlike the way
we move away from neighboring galaxies. The analogy is not perfect, nor should
one try too hard to make it so\footnote{The main difference is that spacetime
has no boundaries in the Big Bang theory while the ``Now" assumed here
constitutes a clear boundary. Still, the Big Bang itself is a boundary in time
(Hawking's \cite{Hawking96} attempt to eliminate it has not been generally
accepted). Black holes constitute boundaries too. Moreover, it is not clear why
boundaries should be considered a disadvantage for a theory.}, but the idea of
an expanding time seems to have a striking accord with the universe's spatial
expansion.

\proclaim{Consequence
2:}{The universe's evolution involves the growth of both space and time.
Alongside with the expansion of the spatial dimension, time expands too as the
advancing ``Now" creates more events together with their associated
spacetime.}

\section{
INFINITY OF TIMES AVOIDED}

Cosmology gives us another valuable clue for dealing with
an old problem. Most theorists avoided Becoming because it seemed to inevitably
entail an endless series of higher and higher time parameters. For if the
``Now" moves along time, than time itself constitutes merely a dimension
for this movement, and an additional time must be assumed for this motion to
occur.

Cosmology, however, has dealt with a similar problem. The
question ``what happened before the Big Bang?" is routinely dismissed as
meaningless by pointing out that ``before" entails time and time itself
was created in the Big Bang. Yet, several models invoked some
``pregeometry" which existed ``before" the Big Bang.\cite{PW75} The
validity of these speculations does not concern us here, but the basic idea is
useful: The primordial geometry does not have to be the same as our present
geometry, but of a more primitive kind, characterized by different axioms, and
thus no infinite series of geometries is entailed.

Similarly for our case, there is no need to invoke a yet
higher dimension for the development of spacetime, because this development can
be of a more primitive kind. Recall that Presentism, the model rivaling the
Block Universe, makes a self-consistent assertion: Time is nothing but change,
``the fourth dimension" being merely a metaphor. Most physicists dismiss
this option, and so do we, as it does not accord with relativity theory. But
this reason does not apply for the dynamics of spacetime itself. If spacetime
is subject to dynamics, such as growth in the future direction, there is no
reason to assume that this dynamics is also subject to the laws of relativity.
Velocities may be infinite, absolute simultaneity may hold, and therefore no
higher dimensionmay
have to be invoked. Bergson's \cite{Bergson11} radical idea about pure change
which transcends any dimensionality can therefore be neatly integrated with the
relativistic spacetime, simply by assigning the former a more fundamental
status:

\proclaim{Consequence
3:}{Change is more fundamental than space and time. Relativistic spacetime is
subject to changes, such as the growth of its spatial and temporal dimensions.
This is pure change, i.e., one state coming into existence after another, not
subject to relativistic constraints, hence possessing no dimensionality
whatsoever.}

\section{
RELATIVITY DYNAMIZED: INTERACTION PRECEDES SPACETIME}

The Big Bang model has asserted what a few philosophers
have earlier speculated: Space and time are not primary entities but
derivatives of the unique event of creation. Our theory goes one step further
to suggest that this creation of spacetime is continuous, thus affirming the
na\"ive impression that every moment is a new creation.

Next, therefore, let us examine the relativistic
principles governing spacetime within the new framework. Here, the Becoming
Assumption seems to give these principles an appealing twist. Recall that for
spacetime to be conceivable, there has to be not only a body, but two bodies at
least, for it takes two bodies to distinguish between relative rest and motion
\cite{Mach60}. Our next postulate is therefore taken from relativity:

\proclaim{Postulate
C:}{There is no absolute motion or rest. All velocities are relative.}

In fact, Mach went further to argue that all effects of
inertia on a body -- rest, motion and even acceleration -- stem from the mere
presence of matter in the universe. In other words, any kinematic state is due
to some interaction. These arguments fit in naturally within the Spacetime
Dynamics theory:

\proclaim{Consequence
4:}{The interaction between bodies precedes the advance of the ``Now."
First, bodies interact outside spacetime. Then, as the ``Now" advances, a
new spacetime zone is formed around the events created by this interaction,
elongating the interacting bodies' world-lines and determining the
spatiotemporal relations between them. Position, momentum and even acceleration
are relative because they arise due to interactions prior to the formation of
the spacetime within which they occur.}

\begin{figure}
[ht]

\label{fig:exp}

\centerline{\epsfig{file=
block.eps, width=4.0cm}} %100 percent

\vspace*{12pt}

\fcaption{Block
Universe model.}

\end{figure}

\begin{figure}
[ht]

\begin{minipage}[t]{0.35\linewidth}

\centerline{\epsfig{file=
becoming-1.eps, width=4.0cm}} %100 percent

\vspace*{12pt}

\fcaption{
Initial state.}

\end{minipage}%

\begin{minipage}[t]{0.35\linewidth}

\centerline{\epsfig{file=
becoming-2.eps, width=4.0cm}} %100 percent

\vspace*{12pt}

\fcaption{Interaction
precedes spacetime.}

\end{minipage}%

\begin{minipage}[t]{0.35\linewidth}

\centerline{\epsfig{file=
becoming-3.eps, width=4.0cm}} %100 percent

\vspace*{12pt}

\fcaption{
New spacetime region is created.}

\end{minipage}

\end{figure}

%\begin{figure}

%\label{fig:exp}

%\begin{center}

%\includegraphics[scale=0.6]{block.eps}

%\caption{Block
Universe model.}

%\label{fig:block}

%\end{center}

%\end{figure}

%\begin{figure}

%\centering

%\subfigure[Initial
state.]{

%\includegraphics[width=0.30\linewidth]{becoming-1.eps}}

%\hfill

%\subfigure[Interaction
precedes spacetime.]{

%\includegraphics[width=0.30\linewidth]{becoming-2.eps}}

%\hfill

%\subfigure[New
spacetime region is created.]{

%\includegraphics[width=0.30\linewidth]{becoming-3.eps}}

%\caption{Spacetime
Dynamics where the ``Now" advances}

%\label{fig:becoming}

%\end{figure}

Figures 1 and 2-4 portray this hypothesis, contrasting
the Spacetime Dynamics theory with the Block Universe. Of course, no serious
attempt is made to portray what occurs beyond spacetime or in the presumed
pre-spacetime interaction.

Interestingly, the problem of nonlocality that besets
Mach's principle is not a hindrance in the present framework. If the initial
interactions take place outside spacetime, distances do not matter and the
entire matter of the universe can affect any body. Rosen \cite{Rosen94}
proposed a similar hypothesis.

The relativistic $c$ invariance,

\proclaim{Postulate
D:}{The velocity of light is the same in all reference frames.}

\noindent

is amenable to a similar explanation. We recall that $c$
is the velocity of all interactions mediated by zero mass bosons, {\it
e.g.~}electromagnetic and gravitational. Here again, the fact that a certain,
privileged velocity is rendered by relativity as more basic than space and
time, strikingly accords with our assumption that spacetime is not a primary
ingredient of physical reality. Rather, perhaps,

\proclaim{Consequence
5:}{The spacetime of every reference frames is {\it formed} by the
gravitational/electromagnetic interaction of that reference frame with its
environment. These interactions, which occur in the pre-spacetime stage,
determine the spatio-temporal distances between the events, such that the speed
of light always appears the same.}

We have thus elevated Mach's epistemological principle to
an ontological hypothesis: It is not only in our thinking, but in reality,
during Becoming, that {\it interaction precedes space, time, position and
momentum.}

Dynamizing Mach's principle, turning it into a real
component of Becoming, offers a deeper explanation not only to the principles
of relativity theory but to quantum phenomena as well. ``Superposition,"
the most fundamental ingredient of QM, denotes the coexistence of several
mutually exclusive states, such as many positions of the same particle. Ever
since the discovery of this state it kept posing two problems:

\begin{enumerate}

\item
While superposition of microscopic objects has been demonstrated in numerous
experiments, no macroscopic objects are observed superposed, even though
quantum theory obliges the latter case just as well. A single particle can
apparently traverse two slits at the same time, but a dead-plus-alive cat is
never encountered.

\item
Moreover, even the theoretical possibility of macroscopic superposition entails
a serious problem within the framework of General Relativity. Suppose that a
massive object is superposed. Then, not only its position within space, but the
gravitational field associated with it as well, must be superposed. Now since
gravitation is defined by GR as a curvature of spacetime, an awkward situation
emerges when this curvature is supposed to be superposed. While we can imagine
a superposition of something within spacetime, it is hard to figure out within
what can spacetime itself be in superposition.

\end{enumerate}

Two major attempts were made so far to deal with this
question:

\begin{enumerate}

\item
The Many-Worlds interpretation asserts that the whole wave function of the
Universe splits with every occurrence of superposition. Here too, many
spacetimes are implicitly supposed to coexist within some undefined superspace.

\item
Penrose's hypothesis \cite{Penrose79} suggests that ``collapse" occurs
once the difference between two superposed states, in terms of spacetime
curvature, exceeds that of one graviton.

\end{enumerate}

Hypothesis (2) is bold and ingenious, but there is a more
far-reaching possibility. If

\proclaim{Postulate
E:}{Macroscopic superposition, though obliged by QM, is never observed,}

\noindent

then, perhaps,

\proclaim{Consequence
6:}{Macroscopic superposition occurs just as the microscopic one, but beyond
the advancing ``Now," where spacetime does not exist yet. All macroscopic
phenomena have been genuinely superposed, but collapsed together with the
progression of the ``Now." Superposition does not evolve in empty
spacetime. Rather, it marks the absence of spacetime in the future.}

An interesting affinity now emerges, which perhaps is not
coincidental: Many quantum physicists try to avoid the notion of
``collapse," preferring hidden-variable interpretations of QM, because of
the non-relativistic implications of this collapse and its time-asymmetry. The
advancing ``Now," of course, is also generally dismissed, for reasons
discussed above. Yet collapse remains the simplest explanation for the
difference between micro- and macroscopic phenomena, and the ``Now" keeps
being the most immediate feature of our experience. Perhaps, then, these two
enigmatic phenomena are one and the same?

\proclaim{Consequence
7:}{``Collapse" marks the very advance of the ``Now," by which
several potential future outcomes of a certain state give place to one definite
outcome in the present.}

Once the more difficult phenomenon of macroscopic
superposition has been addressed, the ``ordinary" superposition, occurring
at the microscopic scale, becomes much more natural. We know that

\proclaim{Postulate
G:}{Many quantum oddities (e.g., the EPR and the delayed-choice experiments)
can be interpreted as stemming from retroactive effects of the measurement
backwards in time.}

\noindent

which pose the following restriction on Becoming:

\proclaim{Consequence
8:}{While the ``Now" generally advances forward in time, at the quantum
scale it might move also backwards. Limited spacetime segments, such as the
superposed trajectories of a particle, are sometimes left ``void" by the
general Becoming, to be retroactively filled later by future interactions.}

Our hypothesis is that microscopic superposition differs
from the macroscopic one in that the former occurs within a spacetime already
formed by the surrounding macroscopic bodies, previously collapsed with the
advancing ``Now" and leaving only a few causal chains incomplete.
Measurement, that is, the interaction of the particle's wave function with
other (unsuperposed) objects, fills these chains backwards. The famous
time-symmetry of quantum interactions \cite{ABL64} may indicate that quantum
evolution sometimes proceed forward in the time of Becoming but backwards in
the relativistic $t$. In other words, while the ``Now" generally advanced
forward, it may sometimes ``go back" in the $-t$ direction to fill some
paths which have remained void.

Our hypothesis of a pre-spacetime stage preceding the
formation of every instant is a dynamic version of Rosen's \cite{Rosen94}
notion of a deeper level of reality which is ``fundamentally and predominantly
nonspatial and nontemporal in character."

\section{TIME'S
ARROW ANCHORED: THE ADVANCING ``NOW" IS THE MASTER ASYMMETRY}

Penrose \cite{Penrose94}, in a very bold move,
conjectured that once a theory of quantum gravity is available, one cherished
ideal of physics will be sacrificed, namely, time asymmetry. In other words, a
tiny time-asymmetry may hide in the basic physical interactions. Although
Penrose occasionally endorsed the Block Universe, his heresy accords much
better with the notion of Becoming. The advancing ``Now" is supposed, by
definition, to move forward, hence is the best candidate to be the long
sought-for ``master asymmetry" from which all other time asymmetries
(entropy, black hole formation, K-mesons T-violation, etc.) stem. Moreover, if
future events genuinely do not exist at any ``Now,"quantum indeterminacy is also genuine rather
than reflecting some unobservable hidden variables. Then, by the
Indeterminacy-Asymmetry Entailment \cite{Elitzur99a}, entropy increase
naturally follows.

\proclaim{Consequence
9:}{The advancing ``Now" is the source of all time-asymmetries. Entropy
increases already when different wave functions interact in advance of the
``Now." The consequent formation of spacetime makes these interactions
irreversible.}

In this respect, at least, the Spacetime Dynamics theory
has an undeniable advantage over the Block Universe. In the latter, time arrows
like the thermodynamic entropy increase are merely assumed, as additions to the
four-dimensional spacetime. They are obliged by everyday experience but with no
justification in the theory itself (see \cite{Price96}). In the Spacetime
Dynamics theory, in contrast, indeterminism and entropy increase are necessary
consequences of spacetime's nature.

\section{CLUES
FOR FIELD THEORY: COLLAPSE OF MACROSCOPIC SUPERPOSITION AS THE SOURCE OF
ATTRACTION/REPULSION BETWEEN BODIES}

Let us reiterate our last steps. We speculated that
relative positions and momenta of bodies, with all the resulting relativistic
effects, are due to pre-spacetime interactions, after which, with the advance
of the ``Now," spacetime forms around the new events (Consequence 4).
Then, in the context of quantum mechanics, we speculated that macroscopic
superpositions also occur outside of spacetime, beyond the ``Now" (Consequence
6). As Consequences 4 and 6 propose essentially the same thing, we may venture
to conclude:

\proclaim{Consequence
10:}{The wave function of a macroscopic body creates a genuine superposition in
the pre-spacetime state beyond the ``Now." Several such wave functions,
when interacting outside spacetime, exert ``measurements" on one another,
leading to mutual collapse and to relative positions and momenta. Relativistic
effects are due to these mutual quantum measurements of macroscopic bodies during
the pre-spacetime stage.}

Next, another pair of postulates, one from QM and one
from relativity, may integrate into a new consequence of the Spacetime Dynamics
theory:

\proclaim{Postulate
H:}{When a particles' position is measured and the particle is found not to
reside at that point in space, the entire wave function is affected by this
negative measurement and the likelihood for collapse increases elsewhere.}

This is the familiar result known as ``interaction-free
measurement" \cite{EV93}. It oddly renders the position of a particle a
result of its being measured elsewhere and {\it not found} there. Apparently,
this quantum mechanical peculiarity has nothing to do with the general
relativistic principle

\noindent

\proclaim{Postulate
I:}{Spacetime is curved in the vicinity of mass.}

\noindent

But both phenomena might be unified by a single new
definition of macroscopic collapse within the framework of the Spacetime
Dynamics theory:

\proclaim{Consequence
11:}{When a macroscopic body is superposed at the pre-spacetime stage, its
``collapse" gives rise not only to its position or momentum at some
definite site and time. It also gives rise to all the empty sites in spacetime
where the body {\it could} have been located.}

Again, ``position" gains an entirely new meaning by
this formulation. Rather than a body being located in some empty space, both
the body and its associated spacetime are created by the same wave function.
But now, {\it changes} in relative positions, namely, {\it accelerations}, call
for a new formulation:

\proclaim{Consequence
12:}{Attraction between bodies results from the special configuration of
spacetime around the interacting bodies. There is, so to speak, ``less
space" between attracting bodies. }

Having suggested that, it occurs to us that not only
attraction but repulsion too can be given a new understanding in such a
framework. Repulsion, however, occurs only in electromagnetism and not in
gravity, and the long sought-for unification of the two realms is still far away.
But perhaps the new reformulation, namely attraction/repulsion being due to
special spacetime regions created by the wave functions around the interacting
bodies, can give a hint towards this goal.

\section{SUMMARY
AND APOLOGY}

The omnivorous synthesis we proposed here originates from
a twofold motivation. First, we find the Block Universe extremely odd. Second,
many unresolved riddles in physics are obviously related to the nature of time,
indicating that something essential is still missing in the relativistic
account. Especially QM seems to keep telling us that the idea of a fixed,
objectively existing future is obscure metaphysics. We therefore suggested
adding Becoming to the existing postulates of theoretical physics.

Trying to preserve the essential features of both
relativistic time and the idea of Becoming, we integrated them in a picture
which ascribed pure change, without dimensionality, to spacetime itself, while
relativity theory holds within that spacetime, thus becoming a special case of
the Spacetime Dynamics theory. Applying Mach's principles, we concluded that
Becoming involves not only the growth of world-lines but also the growth of
spacetime itself in the future direction, in perhaps nontrivial resemblance
with spacetime's spatial expansion in the Big Bang model. In other words,
whereas present-day cosmology invokes one unique event of the creation of
spacetime from nothing, we propose that at every instant, a new segment of
spacetime is created, added to the universe's history.

Then, following Mach's principles and the principles of
special relativity, we gave precedence to events over space and time, and
precedence to relations over events. Consequently, we proposed that relative
positions and momenta are formed in the pre-spacetime stage of every instant,
ahead of the advancing ``Now." Next, from the viewpoint of QM, addressing
the apparent absence of macroscopic superpositions, we proposed that such
states also exist in the pre-spacetime stage. Our next speculation, then,
proposed a unification: It is the wave-functions of macroscopic objects that
interact with one another beyond the ``Now," so as to establish relative
positions and momenta. Spacetime, according to this speculation, is formed only
after the interactions. Applying Machian thinking even further, we suggested
that the collapsing wave functions, upon measuring one another, create both the
bodies and their associated spacetime. Thus, ``position" and
``momentum" gained an entirely new meaning. But then, perhaps even the
phenomena of attraction and repulsion can get a new twist in this paradigm, by
assuming that bodies created different configurations of spacetime between them
so as to become closer or farther. From another perspective, that of thermodynamics,
time's asymmetry, rather than being a fact-like feature of physical reality
added ``by hand" to the physical account of spacetime, became, together
with indeterminism, part and parcel of it.

We anticipate the objections by which the Spacetime Dynamics
theory may be dismissed, as we are painfully aware of them ourselves. At this
stage the theory is vague, relying too much on intuitive guesses, lacking
formal rigor and offering no testable predictions. If we venture to propose it
nonetheless, it is in protest against the dearth of theorizing in current
theoretical physics, dearth which we find, particularly in this centenary of
the Annus Mirabilis, unacceptable. Physicists rarely dare to propose
unconventional ideas nowadays, despite growing discontent with the prevailing
models of spacetime, quantum, and the universe. It is time to move on. New
hypotheses, even highly tentative, provide the best impetus for such a move.

Particularly odd in this respect is the impoverishment of
the superstring models. While they reasonably seek to revise the account of
spacetime for a better understanding of matter and energy, they rarely bother
to address the ``old" riddles of QM such as wave-particle duality,
non-locality and macroscopic superposition. It is highly unlikely that a theory
that ignores these riddles will ever come up with the long waited-for
unification of relativity and quantum theories.

Even odder is superstring theories' muteness about the
nature of time. In marked contrast with their lavishness concerning space --
adding many hidden spatial dimensions -- they leave time, with all its
enigmatic features such as transience and asymmetry, as ill-understood as ever.
We, in contras, believe that even in the above sketchy account we were able to
point out the enormous theoretical potential of the Becoming Assumption, as it
so naturally provides a hidden time within which possible interactions can
operate on the Minkowski-Einstein spacetime.

Cosmology, on the other hand, has been bolder, exploring
many exotic features of the physical reality that might have existed prior to
the Big Bang. ``Pre-geometries," possessing primitive features that might
lie beneath our familiar geometry, are being studied, and here superstring
theories do yield important insights. Our modest contribution in this respect
is the proposition that {\it the Big Bang is incessant.} Every new instant is a
genuine creation {\it ex nihilo} of another segment of spacetime together with
its events, just as the Big Bang is supposed to have been at the beginning of
the universe. Let, then, all the speculations about the conditions that
preceded the Big Bang be applied the unfolding of the next moment. Profound
insights might emergefrom
such an attempt.

It is to the future, which we believe to be really
undetermined, that we relegate the final judgment on this proposal.